Total order

Order whose elements are all comparable

In mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation ≤ {\displaystyle \leq } on some set X {\displaystyle X} , which satisfies the following for all a , b {\displaystyle a,b} and c {\displaystyle c} in X {\displaystyle X} : a ≤ a {\displaystyle a\leq a} (reflexive). If a ≤ b {\displaystyle a\leq b} and b ≤ c {\displaystyle b\leq c} then a ≤ c {\displaystyle a\leq c} (transitive).

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